The area bounded by the curve y = sin(x) and y = cos(x) for sin(x) = cos(x) as point of intersection is equal to 2√2.
Area bounded by the curve y = sin(x) and y = cos(x).
Point of intersection for sinx = cosx
⇒ x = π/4 and 5π/4
Required area
= [tex]\int_{\frac{\pi }{4} }^{\frac{5\pi }{4}}[/tex]( sinx - cosx)dx
= ( -cosx - sinx ) [tex]|_ {\frac{\pi}{4} }^ {\frac{5\pi}{4} }[/tex]
= [ -cos(5π/4) - sin(5π/4) ] - [ -cos(π/4) - sin(π/4) ]
= [ -( -1 / √2 ) - (-1 / √2 ) ] - [ -1 /√2 - 1 /√2 ]
= ( 1 + 1 ) / √2 + ( 1 + 1 ) / √2
= ( 2 + 2 ) / √2
= 4 /√2
= 2√2
Therefore, the area bounded by the given curve is equal to 2√2.
The given question is incomplete, I answer the question in general according to my knowledge:
find the area of the region bounded by the curves y = sin(x), y = cos(x), where solution the points of intersection occur when sin(x) = cos(x), that is, when x = π/4 and 5π/4.
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Curt and Melanie are mixing blue and yellow paint to make seafoam green paint. Use the percent equation to find how much blue paint they should use. Give two decimal places.
1.05 quarts of blue colors paint they mixed to make seafoam green paint.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given figure, total quantity of paint is 1.5 quarts.
70% of blue paint and 30% of yellow paint.
Let the quantity of blue paint be x.
Now, x =70% of 1.5
x =70/100 ×1.5
x =0.7×1.5
x =1.05 quarts
Therefore, 1.05 quarts of blue colors paint they mixed to make seafoam green paint.
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In the triangle below,
x= [? ]°. Round to the nearest
tenth.
9 cm
90⁰
17 cm
19
After solving the equation the triangle given in question the 63.8°.
What is triangle?A triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry and is very versatile as it can be used to create many other shapes and structures. Triangles are generally classified by the length of their sides, which can be equal (an equilateral triangle), longer in one side than the other two sides (an isosceles triangle) or different in length on all three sides (a scalene triangle). They can also be classified by their angles, which can be acute (the angles are all less than 90 degrees), right (one angle is exactly 90 degrees) or obtuse (one angle is greater than 90 degrees).
x = 63.8°
Using the Law of Cosines, we can calculate the value of x:
x² = 17² + 9² - 2(17)(9)cos(90°)
x² = 289 + 81 - 306
x² = 64
x = √64
x = 8
Therefore, x = 63.8° (rounded to the nearest tenth).
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Is it
1.A
2.B
3.C
4.D
Answer:
26 R 1
Step-by-step explanation:
Solve for x please!!
(x + 1) is a factor of x145 + 3x45 – 4.
True or False
(x + 1) is not a factor of the polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
We have a polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
If (x + 1) is a factor.
Then x = -1 is a zero of polynomial.
Now,
(-1)¹⁴⁵ + 3(-1)⁴⁵ - 4
= -8
Therefore, (x + 1) is not a factor.
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please help me!!! I do not understand this!
an octahedron consists of two square-based pyramids glued together along their square bases to form a polyhedron with eight faces. imagine an ant that begins at the top vertex and walks to one of the four adjacent vertices that he randomly selects and calls vertex a. from vertex a, he will then walk to one of the four adjacent vertices that he randomly selects and calls vertex b. what is the probability that vertex b will be the bottom vertex? express your answer as a common fraction.
The probability that vertex b will be the bottom vertex will be 1/16
The ant has four equally likely possibilities for his initial step from the top vertex, each heading to one of the four vertices close to the top vertex.
When the ant reaches vertex A, he has four equally likely next steps, each heading to one of the vertices next to vertex A.
Only one of these possibilities, however, will send him to the bottom vertex: the one that brings him straight to the bottom vertex.
As a result, the ant's chance of reaching the bottom vertex after two steps is 1/4 * 1/4 = 1/16.
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what percentage smoke something (cigars, cigarettes or both)? b. what percentage smoke neither cigars nor cigarettes? c. what percentage smoke cigars but not cigarettes? d. what is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?
Percentage is a concept used to express a fraction as a part of 100. It is typically expressed as a fraction with a denominator of 100 and is written as a number followed by the percent sign (%). For example, the fraction 3/20 can be expressed as 15%, which means 15 out of every 100. Percentage is a useful concept when comparing two or more values, as it provides a way to measure the relative size of each value. For example, if one group of people has 25% of the total number of votes, this means that they have more votes than the other groups, whose percentages are lower.
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Complete question:
A total of 28% of Americans smoke cigarettes, 7% smoke cigars and 5% smoke both cigarettes and cigars
a. What percentage smoke something (cigars, cigarettes or both)?b. What percentage smoke neither cigars nor cigarettes?c. What percentage smoke cigars but not cigarettes?d. What is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?The number e is named after
?
Write the equation of the line that passes through the points (−1,−7) and (1,7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
During this same time, the digital print manager tracked the number of visits to the website’s homepage. he found that before launching the new marketing plan, there were 4,800 visits. over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week. write an equation to model the relationship between the number of weeks, x, and the number of site visits, f(x).
An equation to model the relationship between the number of weeks, x, and the number of site visits, f(x) is 4800 = a(1.5)^x.
He found that before launching the new marketing plan, there were 4,800 visits.
Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.
Over the course of the next 5 weeks, initial visitor at x = 0, 4800
Increasing factor = 1.5
Equation of the model is given as:
f(x) = a(b)^x
From the question b = 1.5
Now the equation of model is:
f(x) = a(1.5)^x
At x = 0, f(x) = 4800
Now the equation of the model is:
4800 = a(1.5)^x
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a college charges $10,000 per semester for tuition. if that college has two semesters per year, what is the student's lifetime value for a student getting a four-year degree?
The student's lifetime value for a four-year degree at this college is $80,000.
The student's lifetime value for a four-year degree can be calculated as follows:
Determine the cost per semester: $10,000 per semester
Determine the number of semesters for a four-year degree: 4 years * 2 semesters/year = 8 semesters
Multiply the cost per semester by the number of semesters to get the total cost of tuition: $10,000 * 8 = $80,000
Therefore, the student's lifetime value for a four-year degree at this college is $80,000.
It is important to note that this calculation only considers the cost of tuition and does not take into account other costs such as room, board, books, and supplies, which can add significantly to the total cost of obtaining a degree.
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show that 2 mn = 1 m (m n 2 ) 1 n (m n 2 ) and use this identity to obtain the unit fraction decompositions of 2 7, 2 35, and 2 91 as given in the 2/n table in the rhind mathematical papyrus.
The fractions found in the 2/n table in the Rhind Mathematical Papyrus.
2/7 = (m n 2 ) 1 n (m n 2 )
= (2 7 2 ) 1 7 (2 7 2 )
= (14 2 ) 1 7 (14 2 )
= 7 1 7 + 7 1 14
2/35 = (m n 2 ) 1 n (m n 2 )
= (2 35 2 ) 1 35 (2 35 2 )
= (70 2 ) 1 35 (70 2 )
= 35 1 35 + 35 1 70
2/91 = (m n 2 ) 1 n (m n 2 )
= (2 91 2 ) 1 91 (2 91 2 )
= (182 2 ) 1 91 (182 2 )
= 91 1 91 + 91 1 182
Using the identity (m n 2 ) 1 n (m n 2 ) we can decompose the fractions 2/7, 2/35, and 2/91 into unit fractions. For 2/7, we obtain the decomposition 7 1 7 + 7 1 14, for 2/35 the decomposition 35 1 35 + 35 1 70, and for 2/91 the decomposition 91 1 91 + 91 1 182. This matches the fractions found in the 2/n table in the Rhind Mathematical Papyrus.
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In 2009 the average weekly wage of men exceeded that of a woman by $162. The um of their average wage equaled $1476. Write and olve a ytem of equation to determine the average wage of men and of women in 2009
The average wage of men is $819 and of women is $657 in 2009
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Information about the problem:
M = W + 162M + W = 1476M = average wage of menW = average wage of womanTo solve this problem we must establish the equations according to the given data and solve the operations:
M = W + 162 (1)
M + W = 1476 (2)
We have two equations with two unknowns, substituting the value (M) in the second equation, we have:
M + W = 1476
W + 162 + W = 1476
162 + 2W = 1476
2W = 1476 - 162
2W = 1314
W = 1314/2
W = 657
Substituting (W) into one of the equations (M) we have:
M = W + 162
M = 657 + 162
M = 819
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a 20 ft ladder leans against building so that the angle between the ground and the ladder is 60 degrees. how far from the building is the base of the ladder?
Salut/Hello!
Answer: 20 ft
Step-by-step explanation:
We can imagine the ladder, wall and ground as a triangle.
(And because we don't know if our triangle has a 90 degrees angle it means it's an ordinary triangle.)
We know that a triangle that has an angle with 60 degrees means all of its angles have 60 degrees because 180 : 3 angles = 60 degrees which means the triangle is equilateral.
Definition of the equilateral triangle: The triangle that has the 3 side with the exact same length.
From the equilateral triangle we know all sides are equal. If the ladder is 20 ft that means the distance between the building and the base of the ladder (which is actually the base of our triangle) is 20 ft.
I hope it was useful! :]
a triangular park has vertices at a(-1,-1), b(4,4) and c(7,-1). a fountain is to be built that is equidistant from all vertices. find the location d of the fountain.
The fountain should be located at the coordinates (4,2). This is the midpoint of the line segment that connects the vertices a(-1,-1) and c(7,-1). It is also the same distance from b(4,4).
To find the location of the fountain, we first need to find the midpoint of the line segment connecting the vertices a(-1,-1) and c(7,-1). This midpoint is located at the coordinates (4,2). To verify that this is the correct location, we can calculate the distance between the midpoint and each vertex. To do this, we use the distance formula, which is d=√((x2-x1)2+(y2-y1)2). Using the coordinates for the midpoint (4,2) and the coordinates for vertex a(-1,-1), we get d=√((42-(-12))2+((22-(-12))2). This simplifies to d=√((52+52))=√(50)=7.07. We can repeat the same process for the midpoint and vertex b(4,4) and for the midpoint and vertex c(7,-1). In both cases, we find that the distance is 7.07, so the fountain should be built at the coordinates (4,2).
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(Lesson 2.9: Jointly Distributed RVs.) YES or NO? Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1. Are X and Y independent? a. Yes b. No
Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1 is No as well as x and y are not independent
What is variables?
Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.
The joint p.d.f of X and Y is f(x, y)
f(x,y) = cxy/ 1+[tex]x^{2}[/tex]+[tex]y^{2}[/tex] for 0 < x < 1 and 0 < y < 1
marginal p.d.f of x = f(x):
f(x) = {1y_of(x,y)dy
= {1y=0 /cxy/ 1+x+[tex]y^{2}[/tex] dy
Cx/2 ( {1y=0 /2y/1+ [tex]x^{2}[/tex] + [tex]y^{2}[/tex] dy)
Take substitute 1+[tex]x^{2}[/tex]+ [tex]y^{2}[/tex] = t⇒2y dy=dt
Lower limit: y = 0⇒t=1+[tex]x^{2}[/tex]
Upper limit: y=1➡t=1+[tex]x^{2}[/tex]+1
F(x) = cx/2
f 1y= 0 2y
=0 1+2+[tex]y^{2}[/tex]dy)
=Cx/2({1+[tex]x^{2}[/tex]+1dt/t
=1+[tex]x^{2}[/tex]t)
=cx/2(In(t) - ln(1+[tex]x^{2}[/tex])/1[tex]x^{2}[/tex])
=cx/2 (In (1+[tex]x^{2}[/tex]+1))-In(1+[tex]x^{2}[/tex]))
=cx/2 (In (1+[tex]x^{2}[/tex]+1/1+[tex]x^{2}[/tex]))
=Cx (In(1+1/1+[tex]x^{2}[/tex]))
marginal p.d.f of y = f(y):
f(y) = {1x
=0(x,y)dx
= F1x
=0/cxy/ 1+[tex]x^{1}[/tex][tex]y^{2}[/tex]=dx
= cy/2({1x)
=0/2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]dx}
Take substitute 1 + [tex]y^{2}[/tex] + [tex]x^{2}[/tex] = t 2x dx = dt
Lower limit: x = 0
t = 1 + [tex]y^{2}[/tex]
Upper limit: x =1
=t + [tex]y^{2}[/tex] + 1
F(y)=cy/2({1x=0 2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]/dx)
=cy({1+[tex]y^{2}[/tex]+1dt/t
=1[tex]y^{2}[/tex]t/)
=Cy/2((In(t))1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex])
=cy(In(1+[tex]y^{2}[/tex]+1) – In( 1+[tex]y^{2}[/tex]))
=cy(In(1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex]))
=cy/2(In(1+1/1+y2))
Now we have to check for independence.
F(x,y)= cxy/1+[tex]x^{2}[/tex]+[tex]x^{2}[/tex] for0<x<1 and 0<y<1
F(x) = cx/2( In(1+1/1+[tex]x^{2}[/tex])) for 0<x<1
F(y)=cy/2(In(1+1/1+[tex]y^{2}[/tex])) for < y <1
=f(x)*f(y)
=c2xy/4 ( In ( 1+1/1+[tex]x^{2}[/tex] ) *In( 1+1/1+[tex]y^{2}[/tex])) #f(x,y)
F(x,y) #f(x)* f(y) for all x and y
=x and y are not independent.
no is correct answer.
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Identify the values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20.
(5,y1) and (x2,2)
The correct values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20 are,
⇒ y₁ = - 1
⇒ x₂ = 10
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The equation is,
⇒ 3x - 5y = 20
Now, If (5, y₁) is the solution of above equation, then it satisfy the equation.
⇒ 3x - 5y = 20
⇒ 3 × 5 - 5y₁ = 20
⇒ 15 - 5y₁ = 20
⇒ 15 - 20 = 5y₁
⇒ - 5 = 5y₁
⇒ y₁ = - 1
And, If (x₂, 2) is the solution of above equation, then it satisfy the equation.
⇒ 3x₂ - 5y = 20
⇒ 3x₂ - 5×2 = 20
⇒ 3x₂ - 10 = 20
⇒ 3x₂ = 20 + 10
⇒ 3x₂ = 30
⇒ x₂ = 10
Thus, The correct values that create ordered pairs that are solutions to the solutions to the equation are,
⇒ y₁ = - 1
⇒ x₂ = 10
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suppose winston's loud music externalizes a cost onto his neighbor, chloe. suppose winston and chloe decide to solve this problem using the coase theorem. if they are successful, what is a possible result of the execution of this theorem?
The Coase theorem states that if property rights are well-defined and transaction costs are low, then the allocation of resources will be efficient, regardless of the initial allocation of property rights.
If Winston and Chloe successfully apply the Coase theorem to solve the problem of Winston's loud music externalizing a cost onto Chloe, they may reach a mutually beneficial agreement. This could result in either Winston reducing the volume of his music or compensating Chloe for the cost of the externalization, or a combination of both.
The goal is to reach a solution where the costs and benefits are more efficiently allocated between the two parties.
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23. Graph the inequality x≤ 8.
The graph of the inequality is added as an attachment
How to determine the graphFrom the question, we have the following parameters that can be used in our computation:
x≤ 8
The above expression is an inequality that implies that
The value of x does not exceed 8
Next, we plot the graph
See attachment for the graph of the inequality
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que es una computadora cuantica
A quantum computer is a type of computer that uses quantum mechanics.
How do quantum computers work ?Quantum computers use quantum mechanics, a branch of physics that deals with the behavior of matter and energy at the subatomic and quantum scale, to perform operations and solve problems.
Unlike classical computers, which use binary digits (bits) to represent and process information, quantum computers use quantum bits, or qubits, which can exist in multiple states at the same time, allowing for exponentially faster processing of complex computations and simulations. Quantum computers have the potential to revolutionize fields such as cryptography, drug discovery, and artificial intelligence.
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Which could be the scale factor of the following similar figures? (1 point)
The first triangle's sides are 9,9,12
The second triangles sides are 6,6,8
A.) 2/3
B.) 3/4
C.) 1
D.) 3/2
E.) 4/3
Answer:3/2
Step-by-step explanation: just did the test
As all sides have grown by 2/3 times, The scale factor is 2/3. Thus, option A is correct.
What is scale factor?In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.
16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.
Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12
The corresponding sides are
6/9, 6/9, 8/12
When you simply, we get
2/3, 2/3, 2/3
As all sides have grown by 2/3 times, The scale factor is 2/3. Thus, option A is correct.
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A spinner with 7 equal sections
labeled A-G is spun 84 times. How
many times would you expect it to
land on a vowel?
Answer:
24 vowels
Step-by-step explanation:
A B C D E F G
two out of 7 are vowels....you would expect to get 2/7 ths of 84 spins to be vowels
2/7 * 84 = 24 vowels
Each side of a rhombus is 10 cm long and one of its diagonals measures 16cm. Find the length of the other diagonal
The length of the other diagonal is 22.36 cm.
What is diagonals ?Diagonal is defined as a sloping line or the slant line, that connects to the vertices of a shape.
Let's call the length of the other diagonal "d".
Since a rhombus has perpendicular diagonals that bisect each other
we can use the Pythagorean theorem to find the length of the other diagonal:
d^2 = 10^2 + 10^2 = 100
d = sqrt(100) = 10 * sqrt(10) = 10 * 2.236 = 22.36 cm
Therefore, the length of the other diagonal is 22.36 cm.
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how to show that the real exponetial sequence for f[k]=f[kt] is f[k]b^k
The real exponential sequence for f[k]=f[kt] is f[k]=b^k.
What is exponential sequence ?
The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers.
The real exponential sequence for f[k]=f[kt] can be shown to be f[k]=b^k by using the definition of exponential functions. If f[k]=f[kt], then f[k]=f[k-1]t and f[k-1]=f[k-2]t, and so on. By substitution, we have:
f[k]=f[k-1]t
f[k-1]=f[k-2]t
f[2]=f[1]t
f[1]=f[0]t
So we can write:
f[k]=f[k-1]t=f[k-2]t^2=...=f[1]t^(k-1)=f[0]t^k
Next, we can define b as f[0] and substitute it into the above equation:
f[k]=b^k
Therefore, the real exponential sequence for f[k]=f[kt] is f[k]=b^k.
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how can we recognize if two real world quantities can be represented with a reciprocal function in a table of values?
We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x
A new function called the reciprocal function is produced when the reciprocal function is found. These functions have intriguing characteristics and distinctive graphs. We also represent these patterns using reciprocal functions when two expressions are inversely proportional. A constant on the numerator and an algebraic expression in the denominator makes up reciprocal functions.
How to find the reciprocal of a function?
By dividing 1 by the provided number, we can find the reciprocal of a given number. Similar reasoning is used to get a function's reciprocal: we divide 1 by the function's expression.
We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x
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Geometry Dilation
Please help!!!!
Answer:
C' (-2, -2)
D' (-2, 2)
E' (2, 0)
F' (0, -2)
Step-by-step explanation:
A dilation of factor k about the origin is a transformation that enlarges a figure by a factor of k, while keeping the origin fixed.
It means that each point (x, y) on the pre-image is transformed to a new point (kx, ky) in the dilated figure.
Therefore, the rule for a dilation of 2 about the origin is:
(x, y) → (2x, 2y)From inspection of the given diagram, the vertices of the pre-image are:
C = (-1, -1)D = (-1, 1)E = (1, 0)F = (0, -1)Applying the dilation rule (x, y) → (2x, 2y):
C' = (2 · -1, 2 · -1) = (-2, -2)D' = (2 · -1, 2 · 1) = (-2, 2)E' = (2 · 1, 2 · 0) = (2, 0)F' = (2 · 0, 2 · -1) = (0, -2)if p and q vary inversely and p is 30 when q is 6, determine q when p is equal to 60.
using inverse relation, If p= 60, then q= 3x because i find the constant value is 180.
What is the p increases inversely as q equation?P is approximately equal to 1/Q since P has an inverse relationship to Q. x=k/3 for P=x and Q=3. P = k/x when Q = x.
The correlation between bond prices and interest rates is a prime illustration of an inverse connection. Bond prices normally fall with an increase in interest rates, whereas bond prices often rise with a decrease in interest rates.
P×1/q
( formula now) P= K/Q here K is a constant
30= k/6
k=30×6
k= 180
when P is equal to 60 then q=
because constant k=60
60= 180/q
q=180/60
q=3 unit .
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a contractor removed 357 cubic yards of earth from a building site. if the contractor's truck can haul 17 cubic yards per load, how many truckloads were needed?
If the contractor's truck can haul 17 cubic yards per load, then 21 truckloads are needed.
Earth removed from a building site is 357 cubic yards.
A contractor's truck can haul 17 cubic yards per load.
To find how many truckloads were needed, we needed to divide the earth removed from the building site by the contractor's truck capable of hauling.
That is,
The number of truckloads = earth removed from the building site/contractors' truck capable of hauling.
The number of truckloads = 357 cubic yards/17 cubic yards per load
The number of truckloads = 21 truckloads.
Therefore, the required truckloads are 21.
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evaluate the integral. 3 5 arctan 1 x d
The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )
The basic arctan formula can be given by θ = tan-1(Perpendicular / Base). Here, θ is the angle between the hypotenuse and the base of a right-angled triangle.
The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.
= [tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx ; where ([tex]\sqrt{3}[/tex] to 1 )
[tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx = [tex]5\frac{(2\sqrt{3} )ln(2)+2\pi -\sqrt{3} \pi }{4\sqrt{3} }[/tex]
= 5 [tex]\int\limits[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx
= 5 [ x arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )[tex]x_{123}[/tex]
Therefore,
The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )
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